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5-6 days in Copenhagen without a car

We are going to be in Copenhagen in early April and don't want to rent a car. I have heard that the city's public transit is very good for around town and that their train system is pretty good for day trips out of town. Any suggestions for day trip destinations?

A car in Copenhagen would be a millstone, so I'm glad you're dismissing that utterly impractical option.

With a Copenhagen Card for museums and other sites, you can get 3 days (I think) of unlimited public transit: subway/ metro (superlative), buses (superlative) suburban train (ditto) and even a boat cruise.

We used our cards to take us to Frederiksborg castle ("Slot"), which enchanted and amazed us.

There are many other out-of-town options which we were unable to explore in our scant 3-4 days in this wonderful (though pricey) city.

One word of warning about transportation: WATCH OUT for the cyclists.

They have dedicated bike lanes, in which you see dozens, perhaps hundreds of fast-moving and merciless 6 foot tall Arctic blondes of both genders.

On their high-slung bikes the women are Valkyries, erect of posture and steely of gaze. They are OFF the second the light turns green and woe betide whoever wanders into their path.

Copenhagen has a great public transportation system. They have a metro and boat transportation: http://en.wikipedia.org/wiki/Copenhagen_Metro. We were there for 4 days and didn't use our car at all, even though we had a car and paid through the nose to park it.

The best place to rent a bike is Baisikeli, they are an awesome bunch of people who are incredibly helpful, and most proceeds go to building bicycles in Africa ( http://baisikeli.dk/copenhagen/baisikeli-rental ). Just remember to avoid rushhour, if you are not from Amsterdam, it will be very stressfull, no, trust me, it will.

One good daytrip is taking the train to Elsinore (the Kystbanen line) get of at Humlebæk station and take a couple of hours at the Luisiana art museum, one of the best in the world ( http://www.louisiana.dk/ ). from here you can take a few extra stops to Elsinore and walk through the old city to Kronborg castle. If you have more time, on the way back you can get off at Klampenborg and walk through the forest park to the Amusement park "Bakken" ( http://www.bakken.dk/ ) for dinner, very cozy.

Other good day trips are Malmö across the bridge in Sweden, Frederiksborg castle in Hillerød and the old city centre in Køge.

There is also the lesser known option to take Bus 350S or bike to Dragør which is a lovely quaint fishing village a stones throw from Copenhagen. Its also possible to bike north along the coast to the "Bakken" amusement park and Dyrehaven park i mentioned before.